The focus of this research will be on development of quantitative methods based on sound biological principles for the analyses of intermediate lesions on the carcinogenic pathway. Such lesions commonly arise in experimental carcinogenesis model systems, such as the mouse skin and rodent liver initiation-promotion systems. The ultimate goal of the analyses is the estimation of critical biological parameters such as the rate of initiation and the rates of cell division and death of initiated cells. Additionally, biologically-based quantitative analyses should lead to the generation of hypotheses to be tested in future experiments. The classical initiation-promotion experimental models, namely the mouse skin and the rodent liver systems, provide unique challenges to the analyst. In the rodent liver system, quantitative observations on three-dimensional objects, the altered hepatic foci, are made in two-dimensional sections under the microscope. Stereological methods must then be employed in order to reconstruct the three-dimensional picture. In the mouse skin system, premalignant lesions, the papillomas, and malignant lesions are directly visible without having to sacrifice the animal. Thus repeated observations are made on the same animal. This leads to the statistical problem of correlated longitudinal observations. The two-mutation clonal expansion model of carcinogenesis will form the basis of this work. This model, which postulates two rate-limiting steps on the pathway to malignancy and explicitly considers cell division and cell death, has natural interpretation within the initiation-promotion-progression paradigm of chemical carcinogenesis. The first rate-limiting event is identified with initiation, the clonal expansion of initiated cells with promotion, and the second rate-limiting event with progression. Four specific projects are planned. The first project has to do with incorporation of more realistic biological assumptions than have hitherto been used into the two-mutation clonal expansion model. In particular, more realistic mathematical descriptions of cell proliferation kinetics will be investigated. The second project will attempt to relax the strong stereological assumptions that have been made in the analyses of altered hepatic foci. Specifically, the assumption that these foci are perfect spheres will be relaxed. This will allow the application of the two-mutation model to experimental systems, such as the kidney and the pancreas, in which the assumption of spherical foci is untenable. The third project will develop quantitative methods for the analyses of very small altered hepatic foci, which are now being experimentally investigated with the development of the appropriate markers. The fourth project will develop methods for the application of the two-mutation clonal expansion model to the analyses of correlated longitudinal data on intermediate lesions, such as the papillomas arising in mouse skin painting experiments.